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Lattices of choice functions and consensus problems

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  • Bernard Monjardet

    ()

  • Vololonirina Raderanirina

    ()

Abstract

In this paper we consider the three classes of choice functions satisfying the three significant axioms called heredity (H), concordance (C) and outcast (O). We show that the set of choice functions satisfying any one of these axioms is a lattice, and we study the properties of these lattices. The lattice of choice functions satisfying (H) is distributive, whereas the lattice of choice functions verifying (C) is atomistic and lower bounded, and so has many properties. On the contrary, the lattice of choice functions satisfying (O) is not even ranked. Then using results of the axiomatic and metric latticial theories of consensus as well as the properties of our three lattices of choice functions, we get results to aggregate profiles of such choice functions into one (or several) collective choice function(s). Copyright Springer-Verlag 2004

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 23 (2004)
Issue (Month): 3 (December)
Pages: 349-382

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Handle: RePEc:spr:sochwe:v:23:y:2004:i:3:p:349-382

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  1. Monjardet, B., 1990. "Arrowian characterizations of latticial federation consensus functions," Mathematical Social Sciences, Elsevier, vol. 20(1), pages 51-71, August.
  2. Johnson, Mark R. & Dean, Richard A., 2001. "Locally complete path independent choice functions and their lattices," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 53-87, July.
  3. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
  4. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
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Cited by:
  1. Vladimir Danilov & Gleb Koshevoy & Ernesto Savaglio, 2012. "Orderings of Opportunity Sets," Department of Economics University of Siena 660, Department of Economics, University of Siena.
  2. Danilov, V., 2012. "Outcast Condition in the Choice Theory," Journal of the New Economic Association, New Economic Association, vol. 13(1), pages 34-49.
  3. repec:hal:journl:halshs-00408174 is not listed on IDEAS
  4. Olivier Hudry & Bruno Leclerc & Bernard Monjardet & Jean-Pierre Barthélemy, 2004. "Médianes métriques et latticielles," Cahiers de la Maison des Sciences Economiques b04044, Université Panthéon-Sorbonne (Paris 1).
  5. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
  6. Danilov, V. & Koshevoy, G., 2005. "Mathematics of Plott choice functions," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 245-272, May.
  7. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories : An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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